Dual Nature of Matter and Radiation
Dual nature tests the photon model, photoelectric effect, stopping potential, work function, de Broglie matter waves, and electron diffraction. The exam checks whether you distinguish intensity effects from frequency effects and whether you use electronvolt and nanometre shortcuts correctly.
Core rules and concepts
- Photon energy E = h nu = hc/lambda. A useful shortcut is E(eV) = 1240/lambda(nm).
- Photoelectric equation: K_max = h nu - phi, where phi is the work function. Threshold frequency nu0 satisfies h nu0 = phi.
- Stopping potential V0 satisfies eV0 = K_max. Increasing intensity increases photocurrent but not K_max; increasing frequency increases K_max.
- Photon momentum p = h/lambda. de Broglie wavelength lambda = h/p = h/sqrt(2mK) for a non-relativistic particle.
- Electron diffraction and the Davisson-Germer experiment support matter waves.
Worked example
Light of wavelength 400 nm falls on a metal with work function 2.0 eV. Photon energy is 1240/400 = 3.1 eV. Thus K_max = 3.1 - 2.0 = 1.1 eV, and the stopping potential is 1.1 V. If intensity is doubled at the same wavelength, the current doubles but K_max and stopping potential remain 1.1 eV.
Traps that cost marks
- Saying brighter light gives faster photoelectrons.
- Using wavelength instead of frequency in the threshold condition.
- Mixing joule and electronvolt in K_max = h nu - phi.
- Forgetting that stopping potential measures maximum kinetic energy, not average energy.
- Using lambda = h/p for a photon and for a massive particle without noting p is the same concept but calculated differently.